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The computation of overlap coincidence in Taylor-Socolar substitution tiling. (English) Zbl 1455.52021

Summary: Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of the authors [Adv. Math. 226, No. 4, 2855–2883 (2011; Zbl 1219.37013)] to check overlap coincidence. It turns out that the tiling has overlap coincidence. So the tiling dynamics has pure point spectrum and we can conclude that this tiling has a quasicrystalline structure.

MSC:

52C23 Quasicrystals and aperiodic tilings in discrete geometry
37B52 Tiling dynamics

Citations:

Zbl 1219.37013
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Full Text: arXiv Euclid

References:

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